PROOF PERTAINING TO SOME IMPORTANT PROPERTIES OF q-INTEGRAL

Alp N., Sarikaya M. Z., Kunt E., Udak H.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, cilt.55, sa.6, ss.1499-1511, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 55 Sayı: 6
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1216/rmj.2025.55.1499
  • Dergi Adı: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.1499-1511
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

In most studies on quantum integral inequalities, the properties of the Riemann integral were also provided for the quantum integral. Due to the misuse of these properties, many studies include some mistakes. In this paper, counterexamples are given first; the properties that cause mistakes are not provided. Moreover, the correct versions of these properties are proved under some conditions. We believe that this study will be an important reference for authors who study quantum integral inequalities.